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skullpatrol

  • 2 years ago

Does 0.999...=1?

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  1. zzr0ck3r
    • 2 years ago
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    .9999........ is not a number

  2. zzr0ck3r
    • 2 years ago
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    have you taken calculus?

  3. zzr0ck3r
    • 2 years ago
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    http://www.math.com/school/subject2/lessons/S2U2L1DP.html

  4. zzr0ck3r
    • 2 years ago
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    scroll down to number 4, its actaully an easy proof.

  5. zzr0ck3r
    • 2 years ago
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    you will enjoy calculus:)

  6. carson889
    • 2 years ago
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    Here is an algebraic proof of it: 10x = 9.999999... with x = 0.99999... 10x - x = 9.99999... - 0.999999... 9x = 9 Thus, x = 1

  7. zzr0ck3r
    • 2 years ago
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    This question was asked because I was trying to exaplin that inbetween any two numbers is another number, he then said what about .9999999.... and 1, i then tried to explain to him that .99999999.. was not a finite number, then we had this question posted:)

  8. zzr0ck3r
    • 2 years ago
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    there is no amount of 9's that you can write after .9 that will make it equal to 1, but the limit as the amount of 9's goes to infinity is said to equal 1

  9. ByteMe
    • 2 years ago
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    wait... doesn't 0.9999... = 9/10 + 9/100 + 9/1000 + .... an infinite bounded series?

  10. mayankdevnani
    • 2 years ago
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    The number "0.9999..." can be "expanded" as: 0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

  11. mayankdevnani
    • 2 years ago
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  12. mayankdevnani
    • 2 years ago
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  13. zzr0ck3r
    • 2 years ago
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    lol, read this. then you will see the point of the question http://openstudy.com/study#/updates/50ab1ceee4b06b5e49334d38

  14. mayankdevnani
    • 2 years ago
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    So the formula proves that 0.9999... = 1.

  15. mayankdevnani
    • 2 years ago
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    @skullpatrol ok

  16. zzr0ck3r
    • 2 years ago
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    but .99999...is not a number is the point of this topic

  17. mayankdevnani
    • 2 years ago
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    0.999999..... is a no. we have tp prove that it is equal to 1

  18. mayankdevnani
    • 2 years ago
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    *to

  19. zzr0ck3r
    • 2 years ago
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    its a number if you think about convergence, but you can never write 1 in the form .999999999999, read the last question and you will see the point im trying to make

  20. zzr0ck3r
    • 2 years ago
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    its not a finite number.... it can be looked at as a sequence....at infinity then its a number. I told him that between any two numbers is another number, he then said what about .99999999999..... and 1, this is what followed.

  21. zzr0ck3r
    • 2 years ago
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    Its an extended real number in the since that infinity is an extended real number....

  22. mayankdevnani
    • 2 years ago
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    "But", some say, "there will always be a difference between 0.9999... and 1." Well, sort of. Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999...9 and 1. That is, if you do the subtraction, 1 – 0.999...9 will not equal zero. But the point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. (That's not a "criticism", per se; infinity is a messy topic.)

  23. zzr0ck3r
    • 2 years ago
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    right and i dont think he has had calculus...

  24. zzr0ck3r
    • 2 years ago
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    this started with density of rational/irational and archimedes principle on the real line

  25. zzr0ck3r
    • 2 years ago
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    the point is, that there is an infinite amount of numbers between any two numbers a,b where a != b

  26. mayankdevnani
    • 2 years ago
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    hahhaha.. we are just fighting you and me are absolutely right...it's a skull problem..right??

  27. mayankdevnani
    • 2 years ago
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    right?? @zzr0ck3r

  28. zzr0ck3r
    • 2 years ago
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    This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)

  29. zzr0ck3r
    • 2 years ago
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    right:)

  30. mayankdevnani
    • 2 years ago
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    :)

  31. waterineyes
    • 2 years ago
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    0.9999 is approximately equal to 1 but it is not exactly equal.. \[0.999 \approx 1 \qquad \qquad (0.999 \ne 1)\]

  32. mayankdevnani
    • 2 years ago
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    got it @skullpatrol

  33. mayankdevnani
    • 2 years ago
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    this question...lol

  34. mayankdevnani
    • 2 years ago
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    http://www.math.hmc.edu/funfacts/ffiles/10012.5.shtml

  35. Zarkon
    • 2 years ago
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    can you provide a proof of this ... "This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)"

  36. zzr0ck3r
    • 2 years ago
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    no, my analysis teacher said it two days ago. she said the elemnts between 0 and 1 have more mappings than 0-infinity

  37. Zarkon
    • 2 years ago
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    your teacher is either wrong or you have misquoted her

  38. Zarkon
    • 2 years ago
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    the real numbers between 0 and 1 is the same size as the real numbers from 0 to infinity

  39. ParthKohli
    • one year ago
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    \[1 - 0.999\cdots = 0.000\cdots = 0\]

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